This concept is at the limits of speculative science. There two mechanisms that would have the effect of speeding-up time tenfold.
The first was proposed by physicist Robert Forward in that negative mass has the effect of speeding up time relative to everything that outside the region dominated by negative mass.
To quote myself from an earlier answer at Speeding up time?:
Robert L Forward described a negative matter time machine thus:
"Suppose we had a negative matter which is very dense. Time would run
faster near or in the negative mass and we could make a hollow sphere
of dense negative mass to speed up time." (in Robert L Forward, "Far
Out Physics", Analog, August 1975, pages 161 and 163).
This doesn't speed up time in an unlimited way,the speed-up factor is
only square of two faster. This is roughly only forty percent faster.
Forward proves this from basic gravitation equations which look like
they're adapted from equations about the mass of black holes (my
guess!). Forward's article isn't detailed like a scientific paper,
The main drawback to this technique in speeding-up time on a planet is that the planet would have to be surrounded by a shell of ultradense negative matter. The other drawback is that time is only speeded-up a factor of forty percent (40%). This falls well short of tenfold faster.
In the same answer another mechanism for speeding-up time was proposed, based on the work of the physicist R T Jones.
There is another way of creating speeded-up time. It involves special
relativity and travelling at superluminal velocities. R T Jones
published in the American Journal of Physics the possibility that
travel faster than light results in time passing at the rate of the
distance traversed. Basically for every light year a spacecraft
travels one year passes shiptime.
So a FTL spacecraft only has to choose a suitable superluminal
velocity to ensure enough speed-up time can pass. Since this is
plausible science fiction, we can assume there is a chronology
protection principle in this fictional universe to take care of any
causality problems, Namely, there won't be any to worry about.
This superluminal model isn't exactly what the OP had in mind. The planet would have to be moving at a constant velocity of ten times lightspeed (c) to achieve a tenfold rate of time passing.